In-Plane Inextensional and Extensional Vibration Analysis of Curved Beams Using DQM

국문 초록 (Abstract)

편미분방정식 해를 위한 효율적인 방법 중의 하나는 미분구적법이다. 이방법은 복잡한 구조 및 하중에 따른 컴퓨터 용량의 과도한 사용뿐만 아니라, 컴퓨터 프로그래밍의 복합알고리즘 해석상의 어려움 피하기 위해 많은 분야에 적용되어왔 다. 아크축의 비신장 및 신장을 고려한 곡선보의 내평면 진동을, 미분구적법 (DQM)을 이용하여 해석하였다. 다양한 경계조 건과 열림각에 따른 진동수을 계산하였다. DQM의 해석결과는, 비교 가능한 정확한 수학적 해법을 다른 수치해석결과와 비교하였다. DQM은 적은 격자점을 사용하고도 정확한 해석을 보여주었고, 다양한 변화에 따른 새로운 결과를 제시하였다.

다국어 초록 (Multilingual Abstract)

One of the efficient procedures for the solution of partial differential equations is the method of differential quadrature. This method has been applied to a large number of cases to circumvent the difficulties of the complex algorithms of programming for the computer, as well as excessive use of storage due to conditions of complex geometry and loading. In-plane vibrations of curved beams with inextensibility and extensibility of the arch axis are analyzed by the differential quadrature method (DQM). Fundamental frequencies are calculated for the member with various end conditions and opening angles. The results are compared with exact experimental and numerical results by other methods for cases in which they are available. The DQM gives good accuracy even when only a limited number of grid points is used, and new results according to diverse variation are also suggested.

참고문헌 (Reference)

1 J. P. Den Hartog, "The Lowest Natural Frequency of Circular Arcs" 5 : 400-408, 1928

2 R. Hoppe, "The Bending Vibration of a Circular Ring" 73 : 158-170, 1871

3 W. Flugge, "Stresses in Shells" Springer- Verlag 1960

4 R. R. Archer, "Small Vibration of Thin Incomplete Circular Rings" 1 : 45-56, 1960

5 H. Lamb, "On the Flexure and Vibrations of a Curved Bar" 19 : 365-376, 1888

6 E. Volterra, "Lowest Natural Frequency of Elastic Arc for Vibrations outside the Plane of Initial Curvature" 28 : 624-627, 1961

7 F. C. Nelson, "In-Plane Vibration of a Simply Supported Circular Ring Segment" 4 : 517-527, 1962

8 강기준, "In-Plane Vibration Analysis of Asymmetric Curved Beams Using DQM" 한국산학기술학회 11 (11): 2734-2740, 2010

9 강기준, "In-Plane Buckling Analysis of Curved Beams Using DQM" 한국산학기술학회 13 (13): 2858-2864, 2012

10 강기준, "In-Plane Buckling Analysis of Asymmetric Curved Beam Using DQM" 한국산학기술학회 14 (14): 4706-4712, 2013

11 N. M. Auciello, "Free Vibrations of Circular Arches" 176 : 443-458, 1994

12 A. S. Veletsos, "Free In-plane Vibration of Circular Arches" 98 : 311-339, 1972

13 L. C. Rodgers, "Dynamic Stability of Out-of-Plane Motion of Curved Elastic Rods" 24 : 36-43, 1973

14 R. E. Bellman, "Differential Quadrature and Long-Term Integration" 34 : 235-238, 1971

15 U. Ojalvo, "Coupled Twisting-Bending Vibrations of Incomplete Elastic Rings" 4 : 53-72, 1962

16 S. K. Jang, "Application of Differential Quadrature to Static Analysis of Structural Components" 28 : 561-577, 1989

17 K. Kang, "Analysis of a Curved beam Using Classical and Shear Deformable Beam Theories" 12 : 244-256, 1998

18 A. E. H. Love, "A Treatise of the Mathematical Theory of Elasticity" Dover 1944